reduce - Scala : fold vs foldLeft

Question

I am trying to understand how fold and foldLeft and the respective reduce and reduceLeft work. I used fold and foldLeft as my example

scala> val r = List((ArrayBuffer(1, 2, 3, 4),10))
scala> r.foldLeft(ArrayBuffer(1,2,4,5))((x,y) => x -- y._1)

scala> res28: scala.collection.mutable.ArrayBuffer[Int] = ArrayBuffer(5)

scala> r.fold(ArrayBuffer(1,2,4,5))((x,y) => x -- y._1)
<console>:11: error: value _1 is not a member of Serializable with Equals
              r.fold(ArrayBuffer(1,2,4,5))((x,y) => x -- y._1)

Why fold didn't work as foldLeft? What is Serializable with Equals? I understand fold and foldLeft has slight different API signature in terms of parameter generic types. Please advise. Thanks.

Answer 1

The method fold (originally added for parallel computation) is less powerful than foldLeft in terms of types it can be applied to. Its signature is:

def fold[A1 >: A](z: A1)(op: (A1, A1) => A1): A1

This means that the type over which the folding is done has to be a supertype of the collection element type.

def foldLeft[B](z: B)(op: (B, A) => B): B

The reason is that fold can be implemented in parallel, while foldLeft cannot. This is not only because of the *Left part which implies that foldLeft goes from left to right sequentially, but also because the operator op cannot combine results computed in parallel -- it only defines how to combine the aggregation type B with the element type A, but not how to combine two aggregations of type B. The fold method, in turn, does define this, because the aggregation type A1 has to be a supertype of the element type A, that is A1 >: A. This supertype relationship allows in the same time folding over the aggregation and elements, and combining aggregations -- both with a single operator.

But, this supertype relationship between the aggregation and the element type also means that the aggregation type A1 in your example should be the supertype of (ArrayBuffer[Int], Int). Since the zero element of your aggregation is ArrayBuffer(1, 2, 4, 5) of the type ArrayBuffer[Int], the aggregation type is inferred to be the supertype of both of these -- and that's Serializable with Equals, the only least upper bound of a tuple and an array buffer.

In general, if you want to allow parallel folding for arbitrary types (which is done out of order) you have to use the method aggregate which requires defining how two aggregations are combined. In your case:

r.aggregate(ArrayBuffer(1, 2, 4, 5))({ (x, y) => x -- y._1 }, (x, y) => x intersect y)

Btw, try writing your example with reduce/reduceLeft -- because of the supertype relationship between the element type and the aggregation type that both these methods have, you will find that it leads to a similar error as the one you've described.